Leftmost derivation

In formal language theory, a context-free grammar (CFG) is a certain type of formal grammar: a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the rule

${\displaystyle A\ \to \ \alpha }$

replaces ${\displaystyle A}$ with ${\displaystyle \alpha }$. There can be multiple replacement rules for any given value. For example,

${\displaystyle A\ \to \ \alpha }$

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